According to [1]}, Theorem 1.1.1 there are linearly independent functions \(\Psi _{1},\Psi _{2}\colon \mathbb {R}\rightarrow  and Floquet-multipliers \) 1,2 such that \(L\Psi _{j}=0\)  a.e. on \(\mathbb {R}\)  and \(\Psi _{j}(x+2\pi )=\rho _{j}\Psi _{j}(x)\)  for \(j=1,2\) . We define \(\phi _{j}\) , \(j=1,2\)  as the solutions to the initial value problems
\({\left\lbrace \begin{array}{ll}L\phi _1=0,\\\phi _{1}(0)=1,\quad \phi _{1}^{\prime }(0)=0,\end{array}\right.}\quad \text{and}\qquad {\left\lbrace \begin{array}{ll}L\phi _2=0,\\\phi _{2}(0)=0,\quad \phi _{2}^{\prime }(0)=1\end{array}\right.}\) 
